All these cars will religiously follow the speed limit, boxing up roads and not permitting those of us who are in a rush to get around them. The road rage will cause accidents, I guarantee that.
These accidents will likely be mostly minor fender-benders that result in the road-ragers losing their licenses (unless, of course, they get a self-driving car.) Or, That, and you'd also probably see road-ragers driving themselves off the road and into fixed objects. The automatic cars'll generally do a pretty good job of avoiding serious collisions--far better than even a reasonably skillled human driver could.
If a person is so lacking in maturity and self-control that they'd start ramming automated cars for not letting them treat the road as their own personal speedway, it's highly unlikely that these individuals are able to conduct themselves in a mature manner in today's traffic. We're not looking at a substantial net-up of people who have no business driving a car, y'know?